This is a research study intended for patients who have untreated malignant mesothelioma (a type of cancer of the cells lining the lungs). This study focuses on an experimental new form of treatment and is designed to determine the least toxic dose of that treatment. The primary purpose is to learn what dose of the specially marked tumor cells is safe and has acceptable side effects, and to evaluate the body's disease fighting response (immune response) to the treatment (gene therapy).